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Topic: Church integer

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	Church encoding - Wikipedia, the free encyclopedia
		Church encoding is a means of embedding data and operators into the lambda calculus, the most familiar form being the church numerals, a representation of the natural numbers using lambda notation.
		Church numerals are the representations of natural numbers under Church encoding.
		Church booleans are the Church encoding of the boolean values true and false.
	en.wikipedia.org /wiki/Church_integer (446 words)

	PlanetMath: Church integer
		A Church integer is a representation of integers as functions, invented by Alonzo Church.
		The transformation from a Church integer to an integer might be
		This is version 5 of Church integer, born on 2002-03-09, modified 2004-09-18.
	planetmath.org /encyclopedia/ChurchInteger.html (118 words)

	Lambda calculus - Wikipedia, the free encyclopedia
		It was introduced by Alonzo Church and Stephen Cole Kleene in the 1930s; Church used the lambda calculus in 1936 to give a negative answer to the Entscheidungsproblem.
		Originally, Church had tried to construct a complete formal system for the foundations of mathematics; when the system turned out to be susceptible to the analog of Russell's paradox, he separated out the lambda calculus and used it to study computability, culminating in his negative answer to the Entscheidungsproblem.
		Of course, in order to do so, the notion of algorithm has to be cleanly defined; Church used a definition via recursive functions, which is now known to be equivalent to all other reasonable definitions of the notion.
	en.wikipedia.org /wiki/Lambda_calculus (2307 words)

	lambda-calculus - BlueRider.com
		A branch of mathematical logic developed by Alonzo Church in the late 1930s and early 1940s, dealing with the application of functions to their arguments.
		For example, the natural number N can be represented as the function which applies its first argument to its second N times (Church integer N).
		Church invented lambda-calculus in order to set up a foundational project restricting mathematics to quantities with "effective procedures".
	lambda-calculus.bluerider.com /wordsearch/lambda-calculus (171 words)

	integer
		The integers consist of the natural numbers (0, 1, 2,...) and their negatives (-1, -2, -3,...; -0 is equal to 0 and therefore not included as a separate integer).
		The set of all integers is usually denoted in mathematics by Z (or Z in flboard bold,), which stands for Zahlen (German for "numbers").
		Integer datatypes are typically implemented using a fixed number of bits, and even variable-length representations eventually run out of storage space when trying to represent especially large numbers.
	www.fact-library.com /integer.html (428 words)

	* Integer - (Computing): Definition
		Most of the work done on the PC is done with integer information, that is, whole numbers and data that is represented by whole numbers...
		The integer N is represented as a which applies a given function N times to a given expression...
		MMX is a new set of instructions (57 new integer instructions, four new data types, and eight 64 bit registers), which expand the capabilities of the CPU...
	en.mimi.hu /computing/integer.html (744 words)

	MISCELLANEOUS DOCTRINAL AND ETHICAL ISSUES
		All expenses, church building maintenance, staff salaries, support for missionaries and para-church services, have to be entertained by the church members including the paid staff members themselves who give their anonymous “tithe” back to the church.
		The truly integer person is willing to alter his or her theological views also in the future, should he or she feel that the standard of seeking after truth couldn’t be met by where he or she is into at a given moment.
		The truly integer person is trusting God that He will honor that attitude and guide him or her to the right place of ministry after maybe suffering disadvantages for keeping to that truth-seeking integrity.
	www.reformation.to /miscellaneous.htm (2948 words)

	PlanetMath: lambda calculus
		-calculus) was invented in the 1930s by Alonzo Church, as a form of mathematical logic dealing primarly with functions and the application of functions to their arguments.
		For instance, Church integers are used as a substitute for actual constants representing integers.
		Cross-references: Russell's paradox, string, degree, languages, functional, combinatory logic, equivalent, associativity, reduced, integers, Church integers, Variables, specifications, constants, arguments, functions, logic
	planetmath.org /encyclopedia/LambdaAbstraction.html (243 words)

	Parish church
		A parish church, in Christianity, is the church which acts as the religious centre of a parish, the basic administrative unit of episcopal churches.
		The church building reflects this status, and there is considerable variety in the size and style of parish churches.
		Many villages in Europe have churches that date back to the Middle Ages, but all periods of architecture are represented.
	www.kiwipedia.com /en/parish-church.html (247 words)

	[No title]
		Both the integers and the operations on them are represented as terms in the pure untyped lambda-calculus.
		All Church numerals have a property that (cn I) is I: the identity combinator is a fixpoint of every numeral.
		It takes an integer and three terms and returns one of them depending on the sign of the number.
	okmij.org /ftp/Computation/lambda-calc-div-neg.txt (999 words)

	Church integer - Computing Reference - eLook.org
		A representation of integers as functions invented by Alonzo Church, inventor of lambda-calculus.
		The integer N is represented as a higher-order function which applies a given function N times to a given expression.
		A Haskell function to return a given Church integer could be written:
	www.elook.org /computing/church-integer.htm (97 words)

	[No title] (Site not responding. Last check: 2007-09-16)
		A \emph{Church integer} is a \htmladdnormallink{representation}{http://planetmath.org/encyclopedia/GroupRepresentation.html} of \htmladdnormallink{integers}{http://planetmath.org/encyclopedia/Integer.html} as \htmladdnormallink{functions}{http://planetmath.org/encyclopedia/Function.html}, invented by Alonzo Church.
		An integer $N$ is represented as a \htmladdnormallink{higher-order function}{http://planetmath.org/encyclopedia/HigherOrderFunction.html}, which applies a given function to a given expression $N$ times.
		\end{rawhtml} The \htmladdnormallink{transformation}{http://planetmath.org/encyclopedia/Transformation.html} from a Church integer to an integer might be \begin{verbatim} unchurch n = n (+1) 0 \end{verbatim} Thus the \texttt{(+1)} function would be applied to an initial value of $0$ $n$ times, yielding the ordinary integer $n$.
	www.ma.utexas.edu /~jcorneli/e/work%20folder/massive/ChurchInteger.tex (105 words)

	sciforums.com - Should the Bible get a 3rd Testament?
		But because the church perceived its risen Lord as a living Lord, even his words could be adjusted or adapted to fit specific church needs.
		Faced with heresy and claims to late revelations, the early church was constrained to retain the historical dimension of its faith,the ephapax, or the “once for all,” revelation of God in Jesus Christ.
		The concept of inspiration was not decisivein the matter of demarcation because the church understood itself as having access to inspiration through the guidance of the Spirit.
	www.sciforums.com /showthread.php?t=38198 (2255 words)

	sciforums.com - The Dispensation of Divine Revenge
		To demonstrate that the Church does not have an excessive wealth, the spate of Lawsuits against the Church as forced the closings of many hospitals and parochial schools.
		When people speak of the Church having 'millions' of dollars, as though that is a great deal of money, they need to consider that economic prudence requires that Trustees for Charity NEVER spend their Principal, but only the INTEREST on their Rents and Investments.
		Unlike Protestantism, the Catholic Church does not implore its Congregations to Selfishness and actively promote slavery, as the Protestants did in the past, and exploitation in order to raise the level of tithes it collects.
	www.sciforums.com /showthread.php?p=648283 (1780 words)

	Church numeral - Enpsychlopedia (Site not responding. Last check: 2007-09-16)
		A Church numeral is a representation of a natural number as a function, invented by Alonzo Church as part of his lambda calculus.
		In similar fashion, all recursive functions are representable in the lambda calculus (are "λ-definable") using Church numerals.
		The transformation from a Church numeral to an ordinary numeral might be
	www.grohol.com /psypsych/Church_integer (473 words)

	RI-125i 'Integrity comes from "Integer"' (Site not responding. Last check: 2007-09-16)
		The word INTEGER is still in use in continental European languages, but in English the word is rare (seldom), or obsolete.
		In English usage, the word 'integer' was used to mean 'whole', or 'entire', from 1509, and from 1644 also used to mean 'marked by moral integrity'.
		In today's German, the word 'integer' refers to a person who has not been corrupted, and also describes someone who is not willing to let himself be corrupted.
	www.insolitology.com /topten/koostrenite/ri-125i.htm (180 words)

	Church integer -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-09-16)
		The natural number n is represented as a (Click link for more info and facts about higher-order function) higher-order function, which takes a function f as argument and returns the n-fold composition f o f o...
		For example, in (Click link for more info and facts about Haskell) Haskell, a (A mathematical relation such that each element of one set is associated with at least one element of another set) function that returns a particular Church integer might be
		In (An elaborate and systematic plan of action) Scheme, one simple expression of the Church integers is as follows:
	www.absoluteastronomy.com /encyclopedia/C/Ch/Church_integer.htm (260 words)

	Church integer (Site not responding. Last check: 2007-09-16)
		A Church integer is a representation of naturalnumbers as functions, invented by Alonzo Church as part of his lambda calculus.
		The natural number n is represented as a higher-order function, which takes afunction f as argument and returns the n-fold composition f o f o...
		For example, in Haskell, a function that returns a particular Church integer mightbe
	www.therfcc.org /church-integer-156588.html (163 words)

	Errata 1 to 3
		Line -n, where n is a positive integer, refers to the nth line from the bottom of a page.
		In fact, that proof, judged by our authors to be too long to be included in the text, is philosophically better than the one we gave in class, based on the completeness theorem.
		It is not really satisfactory to give a semantic proof of such a basic syntactic tool at such an early stage in the treatment of a logical system.
	www.math.yorku.ca /Courses/9798/Math2090/errata1to3/errata1to3.html (1931 words)

	[No title] (Site not responding. Last check: 2007-09-16)
		# num2church.sed ### convert the input integer to church numeral form ### 0 = (\f.(\x.x)) ### 1 = (\f.(\x.(f x))) ### 2 = (\f.(\x.(f (f x)))) ###...
		### n = (\f.(\x.(f^n x))) ### sanity check input # clear whitespace s/[[:space:]]//g # kill leading zeros : zeros s/^0\(.\+\)$/\1/ t zeros ### should be an integer /^[[:digit:]]\+$/b start s/.*/bad input/ b end :start ### have three segments ###
		# church is easy # (slow) s/^\([^]\+\)\([^]\+\)\(.(\\x\.\)\([^)]\+\)\(.\)/\1\2\3(f \4)\5/ s/^\([^]\+\)\([^]\+\)(\\f.(\\x.\(.\)))/\1\2(\\f.(\\x.(f \3)))/ # current is harder # use rules like (1:0) = 10, and (4+1) = 5 # add one s/^\([^]\+\)\([^]\+\)\(.\)/\1(1+\2)\3/ :add # reduce addition # if (1+n)
	www.sarg.ryerson.ca /~cmwilson/code/sed/num2church.sed (167 words)

	[No title]
		One of the techniques is more ; theoretical; the other leads to rather practical operations on ; arbitrary integers.
		All ; Church numerals have a property that (cn %I) is %I: the identity ; combinator is a fixpoint of every numeral.
		The result of applying ; %pred1p to any non-zero Church numeral does not depend on the choice ; for term-M. It is only when %pred1p is applied to %c0 that the ; meaning of term-M is revealed: ; (%pred1p %c0) ;==> (L f (L x term-M)) ; Therefore, term-M must be (-1 f x)!
	okmij.org /ftp/Computation/lambda-arithm-neg.scm (780 words)

	House of Mercy
		The dyadic qualities of the Churches is numerated to Fourteen (14.) The number Fourteen (14) when referenced to the dualistic nature of the Material Plane (2) reflects that of the Churches (7.) 14÷2=7.
		There is a tendency to associate the Churches with the Planetary attributes as a correlation to the Chakras by dint of the numerical similarities.
		Additionally, the emphasis needs to be shifted from that of the Churches to that of the Cities, in order to reap the interior meaning of this aspect of the integration.
	rchmi.blogspot.com (1835 words)

	Where Are We Going?
		Although it is no longer polite in most parish meetings to refer to us as sick, the Church italicizes its real views of us when it refuses to ordain qualified lesbians and gays who are honest and when it refuses to encourage all of us to develop homo-loving sexual relationships.
		Thus the Church drives many of us, especially those of us foolish enough to entrust the Church with our soul's safe-keeping, into the safer bushes, adult bookstores, rest stops along the interstates....almost anywhere free from the risk of making whole and personal contacts.
		For almost two millenia the Church has not been very concerned when it has guessed that scores of bishops and other clergy are gay.
	www.rci.rutgers.edu /~lcrew/pubd/wherearewegoing.html (1241 words)

	The Galileo Project \| Library \| Glossary
		Counter Reformation: As dissenting groups split off from the Catholic Church in what came to be known as the Protestant Reformation, the Church began a series of reform measures of their own.
		These reform measures aimed to keep Church members from becoming Protestants, and were known as the Counter Reformation.
		Inquisition: A permanant institution of the Church charged with the eradication of heresies.
	galileo.rice.edu /lib/glossary.html (1678 words)

	aether: Mathematics question (Site not responding. Last check: 2007-09-16)
		It is a matter of historical fact that the Catholic Church is the only international organization run by a group of well educated, dedicated men, which opposes eugenics.
		And the demonic delight the eugenicists feel in attacking the Catholic Church is a mystery too.
		I believe the question I saw asked for the smallest possible integer value of n for the equation to be true.
	bbs.anus.com /ultimatebb.cgi?ubb=get_topic&f=1&t=003025 (2034 words)

	Business Software Review : Article 'Lambda calculus' (Site not responding. Last check: 2007-09-16)
		Intuitively, the number n in lambda calculus is a function that takes a function f as argument and returns the n-th power of f.
		Since most lexical analysis and translation in the various syntaxes of programming languages can be reduced to the lambda calculus, compilers contain lambda translators as modules.
		Stephen Kleene, A theory of positive integers in formal logic, American Journal of Mathematics, 57 (1935), pp 153 - 173 and 219 - 244.
	www.business-software-review.org /DisplayArticleFull44763.html (2415 words)

	History Data Service - Documentation GBHD / mar_1840 (Site not responding. Last check: 2007-09-16)
		The original table also gives numbers of Church of England and other marriages in each individual year.
		The data have been checked by (a) adding values of rd_num as automatically generated sequence numbers, and then comparing these with the actual values as a check against missing rows and (b) summing the number of marriages for individual years and comparing them with tot_mar.
		of marriages 1841-50 according to the rites of the Church of England.
	hds.essex.ac.uk /gbhd/docs/mar_1840_D.asp (432 words)

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